document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142618>Question 1142618</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company that makes corn flex is putting prize coupons in some of the boxes to as a promotional <BR>\n" );
document.write( "strategy. On a certain day, a Supermarket has nine boxes of this product on its shelves and two of <BR>\n" );
document.write( "these nine boxes contain prize coupons. Suppose that the customer who buys a box picks it from the <BR>\n" );
document.write( "shelf at random. The store sells six of these nine boxes on that day. Find out the following <BR>\n" );
document.write( "probabilities, <BR>\n" );
document.write( "a. None of the six boxes sold contains a prize coupon.<BR>\n" );
document.write( "b. At least one of the six boxes sold contains a prize coupon. <BR>\n" );
document.write( "c. Both of the boxes with prizes are sold on that day.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763371 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "a. P(none of the 6 boxes contains a prize coupon)<br><BR>\n" );
document.write( "6 of the 9 boxes are sold: 6 of the 7 boxes with no prize coupon and 0 of the 2 boxes with a prize coupon:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%287%2C6%29%2AC%282%2C0%29%29%2FC%289%2C6%29 ALIGN=MIDDLE  ALT=\"%28C%287%2C6%29%2AC%282%2C0%29%29%2FC%289%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Alternative method....<br><BR>\n" );
document.write( "P(1st box does not contain a prize coupon) = 7/9<BR>\n" );
document.write( "P(2nd box does not contain a prize coupon) = 6/8<BR>\n" );
document.write( "P(3rd box does not contain a prize coupon) = 5/7<BR>\n" );
document.write( "...<BR>\n" );
document.write( "P(6th box does not contain a prize coupon) = 2/4<br><BR>\n" );
document.write( "P(none of the 6 contain a prize coupon) = (7/9)(6/8)(5/7)...(2/4)<br><BR>\n" );
document.write( "You should of course get the same answer by both methods.<br><BR>\n" );
document.write( "b. P(at least one of the 6 boxes contains a prize coupon)<br><BR>\n" );
document.write( "\"At least one\" means \"NOT none of them\"; so 1 minus the answer from part a.<br><BR>\n" );
document.write( "c. P(both of the boxes with prize coupons are sold)<br><BR>\n" );
document.write( "6 of the 9 boxes are sold: 4 of the 7 boxes without a prize coupon and both of the 2 with a prize coupon:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%287%2C4%29%2AC%282%2C2%29%29%2FC%289%2C6%29 ALIGN=MIDDLE  ALT=\"%28C%287%2C4%29%2AC%282%2C2%29%29%2FC%289%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "As with many fairly basic probability problems, it is a good idea to calculate the probabilities for all possible outcomes as a check of your calculations.  If the sum of the probabilities is not 1, your answers are not right.<br><BR>\n" );
document.write( "P(1 of the 2 boxes with a prize coupon is sold)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%287%2C5%29%2AC%282%2C1%29%29%2FC%289%2C6%29 ALIGN=MIDDLE  ALT=\"%28C%287%2C5%29%2AC%282%2C1%29%29%2FC%289%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );